Lunar Gravity-Assist Maneuver As a Way of Reducing the Orbit Amplitude in the Spectrum–Röntgen–Gamma Project

Spectrum–Röntgen–Gamma (SRG) is a space observatory designed to observe astrophysical objects in the X-ray range of the electromagnetic spectrum. SRG is planned to be launched in 2019 by a Proton-M launch vehicle with a DM3 upper stage. The spacecraft will be delivered to an orbit around the Sun–Earth collinear libration point L2 located at a distance of ~1.5 million km from the Earth. Although the SRG launch scheme has already been determined at present, in this paper we consider an alternative spacecraft transfer scenario using a lunar gravity-assist maneuver. The proposed scenario allows a oneimpulse transfer from a low Earth orbit to a small-amplitude orbit around the libration point to be performed while fulfilling the technical constraints and the scientific requirements of the mission.     

Effect of Planetary Eccentricity on Ballistic Capture in the Solar System

Ballistic capture of spacecraft and celestial bodies by planets of the solar system is studied considering the elliptic restricted three body model. A preferential region, due to the eccentricity of the planet and the Sun-gravity-gradient effect is found for the capture phenomenon. An analytical formula is derived which determines the limiting value of the satellite capture eccentricity e_c as a function of the pericenter distance x_p and planet’s true anomaly. The analytic values e_c are tested by a numerical propagator, which makes use of planetary ephemeris, and only a small difference with respect to numerical integration is found. It turns out that lower values of e_c occur when the planet anomaly is close to zero; that is, capture is easier when the planet is at its perihelion. This fact is confirmed by the capture of celestial bodies. It is shown that Jupiter comets are generally captured when Jupiter is in its perihelion region. Ballistic capture is also important in interplanetary missions. The propellant saved using the minimum ballistic capture eccentricity is evaluated for different missions and compared with respect to the case in which the insertion orbit is a parabola: a significant saving can be accomplished.     

Satellite capture by scattering of an existing massive planetary satellite

The dynamics of the satellite–planet system under the influence of the Sun is analyzed in the rotating frame of the planet. This system is described by the well-established, restricted three-body potential. In order to break the capture/escape scenario in temporary satellites, a scattering mechanism by an existing planetary satellite is suggested to account for permanent capture of guest bodies.     

Searching for nonsolar planets

Existing instruments are unable to detect planets about stars other than the Sun but such detection would be important for the theory of origin of our solar system and in the search for extraterrestrial intelligence. Infrared offers an advantage of about 10⁵ over visible light as regards the ratio of power received from star and planet. Infrared interferometry from Earth orbit would allow discrimination against the stellar infrared by the placement of an interference null on the star and a spinning infrared interferometer would modulate the planetary emission to permit extraction by synchronous detection from the background level. The limit to sensitivity will be set by thermal emission from the zodiacal light particles near the Earth's orbit unless the interferometer is launched out of the ecliptic or out to the orbit of Jupiter, in which case instrumental limitations will dominate. Technological developments in several fields will be required as also with astrometry, spectroscopic radial velocity measurement, and direct photography from orbit, three approaches with which infrared interferometry should be carefully compared.     

木星探测轨道分析与设计

研究了与木星探测相关的轨道设计问题.重点关注木星探测轨道与火星、金星等类地行星探测轨道的不同及由此带来的轨道设计难点.首先分析了绕木星探测任务轨道的选择.建立近似模型讨论了向木星飞行需要借助多颗行星的多次引力辅助,对地木转移的多种行星引力辅助序列,使用粒子群算法搜索了2020年至2025年之间的燃料最省飞行方案并对比得到了向木星飞行较好的引力辅助方式为金星-地球-地球引力辅助.结合多任务探测,研究了航天器在飞向木星途中穿越主小行星带飞越探测小行星的轨道设计.最后,给出2023年发射完整的结合引力辅助与小行星多次飞越的木星探测轨道设计算例.     

Spin-induced orbital perturbations for different types of planetary bodies

Using numerical simulations, we studied several coupled translational and rotational solutions of the two-finite-body problem with one spherical and one triaxial body. The aim was to investigate which types of orbits and planetary bodies could produce spin-induced orbital perturbations relevant enough to add to models dealing with other perturbations. To fully assess the strengths and consequences of this perturbation, we did not include any other perturbation even when a more realistic scenario would have required it. Interesting results concern planet–star mass ratios like a hot Jupiter or a super-Jupiter around a star like the Sun or the red dwarf Proxima Centauri. The short-period chaotic effect of the gravitational spin–orbit perturbation on highly eccentric orbits in the vicinity of the Roche limit can be a prominent feature. It should be taken into account when studying the tidal evolution of such a planet or its interactions with any companion in the neighborhood of the star.     

The geometry of impacts on a synchronous planetary satellite

We consider a satellite in a circular orbit about a planet that, in turn, is in a circular orbit about the Sun; we further assume that the plane of the planetocentric orbit of the satellite is the same as that of the heliocentric orbit of the planet. The pair planet–satellite is encountered by a population of small bodies on planet-crossing, inclined orbits. With this setup, and using the extension of Öpik’s theory by Valsecchi et al. (Astron Astrophys 408:1179–1196, 2003), we analytically compute the velocity, the elongation from the apex and the impact point coordinates of the bodies impacting the satellite, as simple functions of the heliocentric orbital elements of the impactor and of the longitude of the satellite at impact. The relationships so derived are of interest for satellites in synchronous rotation, since they can shed light on the degree of apex–antapex cratering asymmetry that some of these satellites show. We test these relationships on two different subsets of the known population of Near Earth Asteroids.     

The disruption of planetary satellites and the creation of planetary rings

The Voyager spacecraft discovered that small moons orbit within all four observed ring systems coincident with the discovery of narrow and dusty rings around Jupiter, Saturn, Uranus and Neptune. These moons can provide the source for new rings if they are catastrophically disrupted by a comet or large meteoroid impact. This hypothesis for ring origins provides a natural mechanism for the ongoing creation of planetary rings. While it relieves somewhat the problem of explaining the continued existence of rings with apparently short evolutionary lifetimes, it raises the problem of explaining the continued existence of small moons, and the coexistence of moons and rings at comparable locations within the Roche zones of the giant planets. This problem has been studied in some detail recently, and the present work is a review of our current understanding of the processes in satellite disruption that pertain to the creation of planetary rings and the collisional cascade of circumplanetary bodies. Significant progress has been made. Narrow rings are produced by disruption of small moons in numerical simulations, and a self-consistent model of the collisional cascade can explain present-day moon populations. Absolute timescales and initial moon populations remain uncertain due to our poor knowledge of the impactor population and uncertainties in the strength of planetary satellites. More pressing are the qualitative issues that remain to be resolved including the nature of reaccretion of the debris and the origin of Saturn's rings.     

Atmospheric thermal structures of the giant planets

Thermal models of planetary atmospheres can be calculated from assumptions of the energy budget of the atmosphere and from the knowledge of the effective temperature of the studied planet. On the other hand, the retrieval of the thermal atmospheric profiles from infrared measurements by means of the numerical inversion of the radiative transfer equation presents the advantages of not requiring such assumptions. The extent of the atmospheric range which can then be sounded is examined and the vertical resolution of the inferred profiles is discussed. Comparisons of thermal models and retrieved thermal profiles are made for the four giant planets. The retrieved profiles lead to brightness temperature spectra which fit all the available infrared measurements fairly well for Jupiter and Saturn but only part of them for Uranus and Neptune. The values of the planetary effective temperatures calculated from the retrieved profiles show that Jupiter, Saturn, and Neptune have strong internal heating sources while Uranus probably has a very small or null one.     

小行星主带上单个行星的质量上限

介绍了N体模拟的Hermite算法,并利用该算法研究了不同质量行星在小行星主带上轨道的演化情况．采用的演化模型是太阳系N体模型(N=7),即把水星、金星、地球的质量加到太阳上,忽略冥王星,同时在小行星主带附近增加一个假想行星,系统演化时间为1亿年．数值模拟显示能够稳定存在于小行星主带上的单个天体的质量上限其量级为10~(25)kg．模拟同时还显示在某些情况下,假想行星与木星之间的低阶共振可以增强系统的稳定性．     

Reassessing the origin of Triton

The origin of Neptune’s large, circular but retrograde satellite Triton has remained largely unexplained. There is an apparent consensus that its origin lies in it being captured, but until recently no successful capture mechanism has been found. Agnor and Hamilton (Agnor, C.B., Hamilton, D.P. [2006]. Nature 441, 192-194) demonstrated that the disruption of a trans-neptunian binary object which had Triton as a member, and which underwent a very close encounter with Neptune, was an effective mechanism to capture Triton while its former partner continued on a hyperbolic orbit. The subsequent evolution of Triton’s post-capture orbit to its current one could have proceeded through gravitational tides (Correia, A.C.M. [2009]. Astrophys. J. 704, L1-L4), during which time Triton was most likely semi-molten (McKinnon, W.B. [1984]. Nature 311, 355-358). However, to date, no study has been performed that considered both the capture and the subsequent tidal evolution. Thus it is attempted here with the use of numerical simulations. The study by Agnor and Hamilton (Agnor, C.B., Hamilton, D.P. [2006]. Nature 441, 192-194) is repeated in the framework of the Nice model (Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F. [2005]. Nature 435, 459-461) to determine the post-capture orbit of Triton. After capture Triton is then subjected to tidal evolution using the model of Mignard (Mignard, F. [1979]. Moon Planets 20, 301-315; Mignard, F. [1980]. Moon Planets 23, 185-201). The perturbations from the Sun and the figure of Neptune are included. The perturbations from the Sun acting on Triton just after its capture cause it to spend a long time in its high-eccentricity phase, usually of the order of 10 Myr, while the typical time to circularise to its current orbit is some 200 Myr, consistent with earlier studies. The current orbit of Triton is consistent with an origin through binary capture and tidal evolution, even though the model prefers Triton to be closer to Neptune than it is today. The probability of capturing Triton in this manner is approximately 0.7%. Since the capture of Triton was at most a 50% event - since only Neptune has one, but Uranus does not - we deduce that in the primordial trans-neptunian disc there were some 100 binaries with at least one Triton-sized member. Morbidelli et al. (Morbidelli, A., Levison, H.F., Bottke, W.F., Dones, L., Nesvorný, D. [2009]. Icarus 202, 310-315) concludes there were some 1000 Triton-sized bodies in the trans-neptunian proto-planetary disc, so the primordial binary fraction with at least one Triton-sized member is 10%. This value is consistent with theoretical predictions, but at the low end. If Triton was captured at the same time as Neptune’s irregular satellites, the far majority of these, including Nereid, would be lost. This suggests either that Triton was captured on an orbit with a small semi-major axisa ? 50R_N (a rare event), or that it was captured before the dynamical instability of the Nice model, or that some other mechanism was at play. The issue of keeping the irregular satellites remains unresolved.     

Source regions and timescales for the delivery of water to the Earth

Abstract— In the primordial solar system, the most plausible sources of the water accreted by the Earth were in the outer asteroid belt, in the giant planet regions, and in the Kuiper Belt. We investigate the implications on the origin of Earth's water of dynamical models of primordial evolution of solar system bodies and check them with respect to chemical constraints. We find that it is plausible that the Earth accreted water all along its formation, from the early phases when the solar nebula was still present to the late stages of gas‐free sweepup of scattered planetesimals. Asteroids and the comets from the Jupiter‐Saturn region were the first water deliverers, when the Earth was less than half its present mass. The bulk of the water presently on Earth was carried by a few planetary embryos, originally formed in the outer asteroid belt and accreted by the Earth at the final stage of its formation. Finally, a late veneer, accounting for at most 10% of the present water mass, occurred due to comets from the Uranus‐Neptune region and from the Kuiper Belt. The net result of accretion from these several reservoirs is that the water on Earth had essentially the D/H ratio typical of the water condensed in the outer asteroid belt. This is in agreement with the observation that the D/H ratio in the oceans is very close to the mean value of the D/H ratio of the water inclusions in carbonaceous chondrites.     

Definitive orbit of minor planet (29) Amphitrite from 91 oppositions 1825--1985 and a new determination of the mass of Jupiter

Minor planet (29) Amphitrite will serve as a target for the first asteroid flyby with NASA spacecraft Galileo on December 6, 1986. It also represents a first priority object for solar system observations with the ESA astrometry satellite Hipparcos which is scheduled to be launched in 1988. In order to meet the high astrometric accuracy requirements, a definitive orbit based on 1,577 observations from 91 apparitions covering the time span 1825 to 1985 is evaluated. (29) Amphitrite moves near to the 3:1 resonance to Jupiter and seems particularly suited for a new determination of the mass of the Jupiter system. A most probable mass value of 1/(1047.369±0.029) solar masses is obtained and the relaibility of this result is discussed.     

Planetary magnetism

The origin and maintenance of planetary magnetic fields are discussed. The discussion is not limited to dynamo theories although these are almost universally favored. Thermoelectric currents are found to be a possible alternative for Jupiter. Two energy sources for dynamos are considered: convection and precessionally induced fluid flow. The earth is the most favorabl planet for a precessionally driven dynamo, although Neptune is a possibility. Jupiter is likely to have a convectionally driven dynamo, as may Saturn, but the relevant properties of Saturn are not yet well known. Conclusions for each planet are given.     

Perturbation of a satellite orbiter by the oblateness of the primary planet

The perturbation of an orbiter around a large satellite of a giant planet (Jupiter, Saturn, Uranus or Neptune) produced by the oblateness of the planet is investigated. The perturbing force of theJ ₂-term (general case) and theJ ₄-term (special case of small eccentricity and inclination) is expanded in an appropriate form and the main term and the parallactic term are given explicitly. The variations of the orbital elements are derived using the stroboscopic method. An example shows that the perturbation of the orbit cannot be neglected.     

Frozen orbits at high eccentricity and inclination: application to Mercury orbiter

We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed by a third body, assumed to lay in the equatorial plane (Sun or Jupiter for example) using a Hamiltonian formalism. We are able to determine, in the parameters space, the location of the frozen orbits, namely orbits whose orbital elements remain constant on average, to characterize their stability/unstability and to compute the periods of the equilibria. The proposed theory is general enough, to be applied to a wide range of probes around planet or natural planetary satellites. The BepiColombo mission is used to motivate our analysis and to provide specific numerical data to check our analytical results. Finally, we also bring to the light that the coefficient J ₂ is able to protect against the increasing of the eccentricity due to the Kozai-Lidov effect and the coefficient J ₃ determines a shift of the equilibria.     

The 1/1 resonance in extrasolar planetary systems

We study orbits of planetary systems with two planets, for planar motion, at the 1/1 resonance. This means that the semimajor axes of the two planets are almost equal, but the eccentricities and the position of each planet on its orbit, at a certain epoch, take different values. We consider the general case of different planetary masses and, as a special case, we consider equal planetary masses. We start with the exact resonance, which we define as the 1/1 resonant periodic motion, in a rotating frame, and study the topology of the phase space and the long term evolution of the system in the vicinity of the exact resonance, by rotating the orbit of the outer planet, which implies that the resonance and the eccentricities are not affected, but the symmetry is destroyed. There exist, for each mass ratio of the planets, two families of symmetric periodic orbits, which differ in phase only. One is stable and the other is unstable. In the stable family the planetary orbits are in antialignment and in the unstable family the planetary orbits are in alignment. Along the stable resonant family there is a smooth transition from planetary orbits of the two planets, revolving around the Sun in eccentric orbits, to a close binary of the two planets, whose center of mass revolves around the Sun. Along the unstable family we start with a collinear Euler–Moulton central configuration solution and end to a planetary system where one planet has a circular orbit and the other a Keplerian rectilinear orbit, with unit eccentricity. It is conjectured that due to a migration process it could be possible to start with a 1/1 resonant periodic orbit of the planetary type and end up to a satellite-type orbit, or vice versa, moving along the stable family of periodic orbits.     

New Challenges to Trajectory Design by the Use of Electric Propulsion and Other New Means of Wandering in the Solar System

The design of spacecraft trajectories is a crucial part of a space mission design. Often the mission goal is tightly related to the spacecraft trajectory. A geostationary orbit is indeed mandatory for a stationary equatorial position. Visiting a solar system planet implies that a proper trajectory is used to bring the spacecraft from Earth to the vicinity of the planet. The first planetary missions were based on conventional trajectories obtained with chemical engine rockets. The manoeuvres could be considered 'impulsive' and clear limitations to the possible missions were set by the energy required to reach certain orbits. The gravity-assist trajectories opened a new way of wandering through the solar system, by exploiting the gravitational field of some planets. The advent of other propulsion techniques, as electric or ion propulsion and solar sail, opened a new dimension to the planetary trajectory, while at the same time posing new challenges. These 'low thrust' propulsion techniques cannot be considered 'impulsive' anymore and require for their study mathematical techniques which are substantially different from before. The optimisation of such trajectories is also a new field of flight dynamics, which involves complex treatments especially in multi-revolution cases as in a lunar transfer trajectory. One advantage of these trajectories is that they allow to explore regions of space where different bodies gravitationally compete with each other. We can exploit therefore these gravitational perturbations to save fuel or reduce time of flight. The SMART-1 spacecraft, first European mission to the Moon, will test for the first time all these techniques. The paper is a summary report on various activities conducted by the project team in these areas.     

The fate of sub-micron circumplanetary dust grains I: Aligned dipolar magnetic fields

We study the stability of charged dust grains orbiting a planet and subject to gravity and the electromagnetic force. Our numerical models cover a broad range of launch distances from the planetary surface to beyond synchronous orbit, and the full range of charge-to-mass ratios from ions to rocks. Treating the spinning planetary magnetic field as an aligned dipole, we map regions of radial and vertical instability where dust grains are driven to escape or crash into the planet. We derive the boundaries between stable and unstable trajectories analytically, and apply our models to Jupiter, Saturn and the Earth, whose magnetic fields are reasonably well represented by aligned dipoles.